DE 196 36 508.2 discloses a radial piston pump with working pistons, wherein the working pistons are accommodated in a cylinder block and driven by means of a driving shaft that projects into a crank space of the cylinder block, and a radial bearing is arranged on the eccentric part of the driving shaft. A piston end that projects radially inwards out of the cylinder block can be acted upon through the bearing shell, said bearing shell being closed in the form of a bottom wall on the side facing the end of the eccentric portion. The bearing shell can execute a rotational movement relative to the driving shaft in dependence on the prevailing friction conditions. In addition, the bearing shell can move into contact with a bottom of the crank space in order to axially support the driving shaft. Because each contact action causes friction and wear between bearing ring and crank space bottom, the efficiency of the motor-pump unit requires improvement.